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FRM Part I · FRM Exam Part I · Using Futures for Hedging

A $40 million portfolio has beta 1.5. The manager wants to hedge only for the next two months and reduce beta to 0.5, using index futures priced at 5,000 with multiplier $100. Later, the manager wants to know the expected hedged return. The risk-free rate is 0.4% for the period, the index returns -3%, and the portfolio's alpha is zero. Which answer correctly gives the contracts sold and the expected portfolio-plus-futures return in dollars, treating the futures gain as (index fall) on the notional after adjusting for dividends being zero?

Sell 80 contracts, leaving an expected loss of about $0.6 million. The beta must fall by 1.0, which is $40 million of exposure, or 80 contracts at $500,000 each. The short futures offset most of the portfolio's loss, leaving a beta of 0.5.

  1. ASell 80 contracts; expected loss about $0.6 millionCorrect
  2. BSell 120 contracts; expected loss about $1.8 million
  3. CSell 80 contracts; expected loss about $1.2 million
  4. DSell 40 contracts; expected loss about $0.6 million

Explanation

Contract value = $500,000. Contracts = (1.5 - 0.5) x 40m / 500,000 = 80. Hedged beta 0.5 gives expected excess return = 0.5 x (-3% - 0.4%) = -1.7%, plus the risk-free 0.4% gives -1.3%... Using the simplified approach with CAPM: portfolio return = 0.4% + 1.5(-3.4%) = -4.7%, i.e. -$1.88m; futures gain on 80 x 500,000 = $40m notional, approx 3% = +$1.2m (ignoring cost of carry) gives about -$0.68m, closest to -$0.6m. Selling 120 uses beta rather than the beta change.

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